1. Field of the Invention
The present invention relates to a mask pattern generating method, a recording medium, and an information processing apparatus.
2. Description of the Related Art
In recent years, a miniaturization of a mask pattern for a semiconductor device has been advanced, and it is being difficult to perform an image dissection of the mask pattern by a projection exposure apparatus. A technique with which a small auxiliary pattern that is not subjected to the image dissection is added to the mask pattern is proposed as a technique for solving the problem. This auxiliary pattern may be referred to as sub-resolution assist features (SRAF).
Japanese Patent Laid-Open No. 2004-221594 discloses a technology for deriving an insertion position of the auxiliary pattern by a numeric calculation. According to the technology, a position where mutual interferences occur on the mask and a position where interferences are mutually cancelled are obtained by the numeric calculation, and an interference map is derived. Then, an auxiliary pattern with which a phase of light that has passed through a main pattern to be transferred to a substrate (such as a wafer) and a phase of light that has passed through the auxiliary pattern with respect to the main pattern are equal to each other is inserted at the position where the interferences occur on the interference map. As a result, the light that has passed through the main pattern and the light that has passed through the auxiliary pattern strongly interfere with each other.
On the other hand, in a partial coherent image formation in an exposure apparatus, a coherence is obtained from information of an effective light source distribution on a pupil plane of a projection optical system, and it is possible to calculate an aerial image from the coherence and a spectrum distribution of the mask pattern (diffraction light distribution). Herein, the coherence refers to a degree of an interference between certain two points on the mask plane. The coherence is represented by a transmission cross coefficient (TCC). The TCC is defined by the pupil plane of the projection optical system and corresponds to the effective light source distribution, a pupil function in the projection optical system, and an overlapped part of complex conjugate numbers of the pupil function in the projection optical system.
According to Japanese Patent Laid-Open No. 2008-040470, the positions of the pupil function in the projection optical system and the effective light source distribution are fixed, and only the positions of the complex conjugate numbers of the pupil function in the projection optical system are set to be two-dimensionally variable to obtain a two-dimensional TCC, so that an approximate aerial image with respect to the main pattern is calculated by using the two-dimensional TCC. Then, the auxiliary pattern is inserted in the vicinity of a peak position of the approximate aerial image.
The interference map described in Japanese Patent Laid-Open No. 2004-221594 and also the approximate aerial image described in Japanese Patent Laid-Open No. 2008-040470 illustrate positions indicating how much the light from the position where the auxiliary pattern exists interferes with the light from the main pattern to intensify and weaken the image of the main pattern. However, these pieces are not data directly indicating how much values image characteristics of the main pattern (for example, a focus depth of the image, a contrast of the image, an ILS of the image, and the like) become in accordance with the position of the auxiliary pattern. The above-described characteristics represent characteristics of the image of the pattern formed on the substrate while the pattern on the mask is illuminated, and the image of the pattern is projected on the subject via the projection optical system to expose the substrate.
For that reason, according to the technologies disclosed in Japanese Patent Laid-Open No. 2004-221594 and Japanese Patent Laid-Open No. 2008-040470, it is difficult to discriminate the values of the image characteristics of the main pattern in accordance with the position of the auxiliary pattern, and the image of the main pattern may not be formed with respect to a target pattern on the substrate at a sufficient accuracy in some cases.